University of Sydney

School of Mathematics and Statistics

Algebraic Geometry Seminar

11:05-12:30 in Carslaw 709 on Wednesday 13 June 2001.
There will be a short break around 11:50

Joost van Hamel

Cohomological obstructions to the local-global principle

When we want to solve equations over a global field (say, a number field, or a function field of a curve), we often start by considering the solutions over the associated local fields. For example, a quadratic form over a number field has solutions if and only if it has solutions over all completions. In other words, the local-global principle holds for quadratic forms.

The local-global principle does not hold in general. There are some well-known obstructions coming from cohomology. In this informal talk I will try to explain how these obstructions work from a geometric/topological point of view, emphasizing the analogy between number fields and function fields of curves.